The Atlantic Club Casino Hotel in Atlantic City NJ, shown here, will shut down on Jan. 13, 2014.

CAMDEN, N.J. — A slowdown brought on by the rapid proliferation of casino gambling in the northeastern United States claimed its first victim in New Jersey on Monday when a federal bankruptcy judge approved the sale and shutdown of Atlantic City’s Atlantic Club Casino Hotel.

The casino, which opened in 1980 as the Golden Nugget and featured then-owner Steve Wynn bringing fresh towels to Frank Sinatra in its commercials, will shut its doors Jan. 13.

Judge Gloria Burns approved a deal that was reached Friday. Two rival casino companies with a presence in Atlantic City, Tropicana Entertainment and Caesars Entertainment, will buy the casino for $23.4 million, essentially strip it for parts and shut it down. The Tropicana will take the slot machines and table games, while Caesars will get the 800-plus-room hotel.

Neither has any interest in operating the business in Atlantic City’s now diminished market. Atlantic City will have 11 casinos after the shutdown.

Competition is a fact of life now for Atlantic City’s casinos, said David Rebuck, director of the New Jersey Division of Gaming Enforcement.

“We realize this is a difficult time for the employees of Atlantic Club and all those who have been part of the history of their operation,” he said.

The Atlantic Club thus became the first Atlantic City casino to close due to the downward spiral touched off seven years ago by the arrival of casinos in neighboring Pennsylvania, which for the first time will now have more casinos (12) than Atlantic City.

“Competition is nothing new for New Jersey and it will be no different in 2014,” Rebuck said.

The elimination of The Atlantic Club should make the market stronger, said Matthew Levinson, chairman of the New Jersey Casino Control Commission.

“No one likes to see a business close, but we are optimistic that market consolidation will result in a stronger and healthier hotel and casino industry in Atlantic City,” he said.

The Atlantic Club is the first Atlantic City casino to close since 2006 when the Sands was shuttered and blown up to make way for a casino that was never built.

Atlantic Club workers packed the courtroom to watch the judge deliver the coup de grace to the casino, where some have worked since the doors opened 33 years ago. Joe Blatcher, a bartender for 30 years at the casino, said he and other workers are particularly distressed that existing Atlantic City casino companies joined together to eliminate a weaker rival.

“It’s a matter of the entire city wanting to eliminate a few properties so that the rest can still exist,” he said. “It seems very suspicious that two casinos can team up to take down another one. It’s like thinning out the herd to survive.”

The judge said there was no evidence during the bankruptcy court auction that any fraud or collusion occurred.

“The worst thing is they’re doing it just to stop competition,” said a tearful Fran Critch, who has been a food server at the casino for 29 years, and who now plans to sell her house because of the grim prospects for other employment in the region.

“Who’s going to hire a 59-year-old server?” she asked.

The deal approved by the judge calls for each of the 1,600 or so workers who will lose their jobs to get a $1,500 severance payment. They can keep what has accrued in their pension plans, but no new contributions will be made.

Caesars has said it has no plans to operate the property as a non-gambling hotel. A spokesman said it intends to distribute some of the building’s equipment among its four Atlantic City casinos — Caesars Atlantic City, Bally’s Atlantic City, Harrah’s Resort Atlantic City and the Showboat Casino Hotel — while considering what to do with the rest.